Eggs and points
Eggs
Eggs only drop from NPC battles. The enemy type decides the family, and the egg already shows which species is inside. A long streak without an egg is compensated automatically.
Eggs can be bought and sold for credits in the Market. Companions themselves cannot be traded.
Companion points
Companion points build up over time on their own. They are used to open eggs and to feed companions, and they cannot be bought or exchanged.
Opening an egg gives the species shown on it. Every egg is a separate companion, even if you already own that species.